相关论文: Interface dynamics equations: their properties and…

We show how the interface curvature autocorrelation function (ICAF) and associated structure factor (ICSF), of relevance in non-equilibrium pattern-formation problems where sharp interfaces are present, provide new and interesting…

There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;,…

We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and…

A family of exponential martingales of a stochastic Laplacian growth problem is proposed. Stochastic Laplacian growth describes a regularized interface dynamics in a two-fluid system, where the viscous fluid is incompressible at a large…

We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…

Many works have studied the Internet topology, but few have investigated the question of how it evolves over time. This paper focuses on the Internet routing IP-level topology and proposes a first step towards realistic modeling of its…

A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…

We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a…

We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding…

This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The…

The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…

A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…

A systematic analytic treatment of fluctuations in Laplacian growth is given. The growth process is regularized by a short-distance cutoff $\hbar$ preventing the cusps production in a finite time. This regularization mechanism generates…

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…

Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of…

The evolution of an initially prepared distribution of micron sized colloidal particles, trapped at a fluid interface and under the action of their mutual capillary attraction, is analyzed by using Brownian dynamics simulations. At a…

We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied : the non-propagating and the propagating one. In the first case, after proving the existence…

The static and dynamic properties of a Cosserat-type lattice interface of finite thickness are studied, so that both displacements and rotational degrees of freedom are taken into account. The model allows considering interfaces with a…

We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T=0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface…